Bridging the Gap - Using AVO to Detect Changes in Fundamental Elastic Constants

Gray, David; Goodway, Bill; Chen, T.

doi:10.3997/2214-4609.201407877

Cited by 17 publications

(11 citation statements)

References 8 publications

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“…To simplify the Zoeppritz equations, many researchers had derived different approximations (Ostrander ; Shuey ; Smith and Gidlow ; Fatti et al . ; Verm and Hilterman ; Gray, Chen and Goodway ; Aki and Richards ; Russell, Gray and Hampson ; Zhang et al . ).…”

Section: Seismic Inversionmentioning

confidence: 99%

Seismic deconvolution and inversion with erratic data

Dai

Chao

Yang

et al. 2018

Geophysical Prospecting

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If there are some erratic data (e.g. outliers), which may arise from measurement error, or other reasons, in seismic data, the seismic deconvolution and inversion need to be implemented in a way that minimizes their effects. However, the deconvolution and inversion methods based on L2‐norm misfit function are highly sensitive to these erratic seismic observations. As an alternative, L1‐norm misfit functions are more robust and erratic‐resistant. In order to find the solution of the inverse problem constrained by an L1‐norm misfit function, an iteratively re‐weighted least squares algorithm is used frequently. However, it is relatively time consuming. In this paper, we propose a new method based on the sparse signal representation theory. The overcomplete dictionary used for the sparse representation of seismic data with erratic data is composed of two bases: a wavelet basis used for representing the seismic data to implement deconvolution and a Dirac basis used for representing the erratic data. In addition, at the stage of seismic inversion after deconvolution, total variation and a priori model are used as the regularization constraint terms to estimate inversion results with a blocky and laterally continuous structure. The new method is successfully tested on the noisy synthetic seismic data with erratic data. Finally, the proposed method is performed on a real seismic data section, and the inversion results are reasonable, i.e. consistent with the geologic structure of the original seismic data. Compared to the conventional sparse deconvolution and inversion method, the proposed method not only eliminates the effect of outliers, but also has highly improved computational efficiency.

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Section: Seismic Inversionmentioning

confidence: 99%

Seismic deconvolution and inversion with erratic data

Dai

Chao

Yang

et al. 2018

Geophysical Prospecting

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“…Gray et al rearranged Aki‐Richards equation in terms of rigidity (µ) and density ( ρ ) along with incompressibility ( λ ) or bulk modulus ( K) as given below.

R_{P P}^{G r a y} (θ) = true[\frac{1}{4} - \frac{1}{2} \frac{β^{2}}{α^{2}} true] \sec^{2} θ \frac{Δ λ}{λ} + \frac{β^{2}}{α^{2}} true[\frac{1}{2} \sec^{2} θ - 2 \sin^{2} θ true] \frac{Δ μ}{μ} + true[\frac{1}{2} - \frac{1}{4} \sec^{2} θ true] \frac{Δ ρ}{ρ}

R_{P P}^{G r a y} (θ) = true[\frac{1}{4} - \frac{1}{3} \frac{β^{2}}{α^{2}} true] \sec^{2} θ \frac{Δ K}{K} + \frac{β^{2}}{α^{2}} true[\frac{1}{3} \sec^{2} θ - 2 \sin^{2} θ true] \frac{Δ μ}{μ} + true[\frac{1}{2} - \frac{1}{4} \sec^{2} θ true] \frac{Δ ρ}{ρ}

Where

Δ K = K_{2} - K_{1}

is change in bulk modulus across the interface,

Δ μ = μ_{2} - μ_{1}

is change in shear modulus across the interface,

Δ λ = λ_{2} - λ_{1}

is change in Lame's constant across the interface,

K = \frac{1}{2...}

…”

Section: Energy Partitioning Spreadsheetsmentioning

confidence: 99%

Spreadsheets for understanding seismic energy partitioning equations

Bangash

Khan

Akhter

2017

Comp Applic In Engineering

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Spreadsheets have come a long way and have become a universal computational tool and a powerful platform for performing scientific and engineering calculations. Their inherent strength lies in integrated storage and manipulation of data, together with a wide range of calculations, charting, and graphics presentation capabilities. These facilities make them ideal tools for prototyping mathematical equations and algorithms that can be adapted for instructional purposes to improve the quality of engineering education. This paper presents a set of spreadsheets that help in understanding the mathematical details behind the Zoeppritz equations and their various approximations that describe the partitioning of seismic wave energy at a planar interface between two homogeneous isotropic and elastic layers of rock. © 2017 Wiley Periodicals, Inc. Comput Appl Eng Educ 25:441–448, 2017; View this article online at http://www.wileyonlinelibrary.com/journal/cae; DOI

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“…More recently, Gray et al (1999) reformulated equation 7 for two sets of fundamental constants: λ sat , μ sat , and ρ sat (the first and second Lamé parameters and density, respectively), and K sat , μ sat , and ρ sat (bulk modulus, shear modulus, and density, respectively), with the shear modulus being identical to the second Lamé parameter), where the relationships between these elastic constants and the saturated compressional velocity (V Psat ) and shear velocity (V Ssat ) are given by…”

Section: The Aki-richards Approximationmentioning

confidence: 99%

“…Thus, Δf is the change in the fluid parameter andf is the average fluid parameter between layers. The key point to note is that, in the Gray et al (1999) formulations, it is the reflectivity associated with saturated bulk modulus and first Lamé parameter that are extracted, whereas in the general reflectivities R f and R μ of equation 17, the fluid and dry parts of reservoir are separated, using the dry rock bulk modulus ratiok dry as a new parameter. As shown in Table 1 of Russell et al (2011) (which shows the inverse ratio, V P ∕V S , squared), the value ofk dry allows us to "tune" equation 16 to the two formulations of Gray et al (1999).…”

Section: The Aki-richards Approximationmentioning

confidence: 99%

Prestack seismic amplitude analysis: An integrated overview

Russell¹

2014

Interpretation

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In this tutorial, I present an overview of the techniques that are in use for prestack seismic amplitude analysis, current and historical. I show that these techniques can be classified as being based on the computation and analysis of either some type of seismic reflection coefficient series or seismic impedance. Those techniques that are based on the seismic reflection coefficient series, or seismic reflectivity for short, are called amplitude variation with offset methods, and those that are based on the seismic impedance are referred to as prestack amplitude inversion methods. Seismic reflectivity methods include: near and far trace stacking, intercept versus gradient analysis, and the fluid factor analysis. Seismic impedance methods include: independent and simultaneous P and S-impedance inversion, lambda-mu-rho analysis, Poisson impedance inversion, elastic impedance, and extended elastic impedance inversion. The objective of this tutorial is thus to make sense of all of these methods and show how they are interrelated. The techniques will be illustrated using a 2D seismic example over a gas sand reservoir from Alberta. Although I will largely focus on isotropic methods, the last part of the tutorial will extend the analysis to anisotropic reservoirs.

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Bridging the Gap - Using AVO to Detect Changes in Fundamental Elastic Constants

Cited by 17 publications

References 8 publications

Seismic deconvolution and inversion with erratic data

Seismic deconvolution and inversion with erratic data

Spreadsheets for understanding seismic energy partitioning equations

Prestack seismic amplitude analysis: An integrated overview

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